You obviously have no chance to "catch" it. But you know it exists.
Once it flies away from the old creepy house, use the grappling hook (from the attic) to climb the tree and collect the egg shells, evidence that it exists. Run them through the DNA tester at the museum.
Yes, you can find proof of The Jersey Devil, Bigfoot, Nessie, and the Chupacabra. (see related question)
Take the shells back to the Mews lab and test them. The DNA analyzer will prove the existence of the Jersey Devil.
You have to look for Bigfoot/Yeti in the Himalayas, the Jersey Devil in New Jersey, the Loch Ness Monster in the Loch Ness in Scotland and the Chupacabra in Puerto Rico.
You need a photo of Nessie at Loch Ness, a tooth from the Chupacabra from Puerto Rico, and egg shells from the nest of the Jersey Devil in New Jersey. (see related solution)
There are 3 you have to prove: Nessie (Loch Ness) Chupacabra (Puerto Rico) New Jersey Devil (New Jersey) You can't get what you need to prove the Yeti, so you are sent to find Bigfoot.
You have to go up in the attic where you will find a racoon. Then, you have to go back down and while you go back down, you will see the Jersey Devil at the window. When you get out the house, you wll see the Jersey Devil.
The Jersey Devil supposedly has hooves like a horse and leathery wings. But no one has ever photographed it.
On poptropica Cryptids Island, the matches are used to light a lantern you get from the monastery (in the Himalayas) which eventually assists you in finding the jersey devil.
When you first start the island and you get the paper about Mews needing the evidence of ONE cryptid to get your reward, you end up needing to search for 4: Bigfoot, the Loch Ness Monster, the Chupacabra, and the Jersey Devil.
After you have confirmed the other three cryptids (Nessie, Chupacabra, and the Jersey Devil), and brought back the inconclusive footprint from the Himalayas, Mews will send you in pursuit of Bigfoot, which is similar to the Yeti.
You will search for evidence in four locations around the globe where cryptids have been observed. As you discover possible clues, you examine them to see if they are genuine. Nessie - at Loch Ness Yeti - in the Himalayas Chupacabra - in Puerto Rico Jersey Devil - in New Jersey (see solution at the related question)
It would really depend on the kids' opinions of what is scary to them or not, but I think that the giant spider on Early Poptropica island and the Jersey Devil on Cryptids island might scare them.